In the league of popular art forms, folk music ranks fairly low, and shadow-puppetry lower still. This ought to leave Matthew Robins, a folk musician who uses shadow puppets on stage, pretty marginalised. Yet Robins has performed at the National Theatre and at Tate Modern – and his own full-length music show, Flyboy Is Alone Again This Christmas, opens tonight at the Barbican.

Robins professes surprise at this success. "I'm not trying to please people, I'm just trying to do something I enjoy." He's certainly a bumbling presence on stage: "People think I play a character because I'm a bit unfocused – I stumble on and fall into the show." His music is indie-orchestral, reminiscent of early Belle and Sebastian, but his lyrics feel artless, unfolding like children's stories. His characters are outsider oddballs: mutant figures called Flyboy and Mothboy, a blundering robot, a wicker cat. The puppets that portray them are roughly scored from black paper; occasionally, the puppeteer's hand strays across the projection screen.

It's this simplicity that makes his shows so appealing, as well as the fact that Robins isn't precious about what he does, laughing as he sings about a character dying or feeling unloved. He's inclusive, too: in the interval for his Christmas show, he'll be providing materials so audiences can make their own shadow puppets, to be incorporated into the second half.

After our talk – in his kitchen, over chocolate cupcakes he baked for the occasion – he shows me his cluttered workroom, lets me play with the puppets for the Flyboy show, and demonstrates how easily he makes them, using a terrifyingly sharp scalpel.

"I've been doing the same thing every day since I was six or seven," he says. "I've never not been sitting down drawing or cutting things out or playing the piano." His parents plied him with art materials when he was growing up in Cornwall; now 30, Robins was recently struck by the thought that his parents sacrificed their own creativity to bring up their three sons. His father was a guitarist – his band, Society's Child, played support slots with Status Quo and the Who – but he sidelined music for a job in an office. Robins suspects his parents, though supportive of his work, "are slightly disappointed I'm not on The X Factor, so I can't buy them a bungalow in Wales".

He has always tried to earn money from art, however. He got his first job at 15, as the pianist at a "posh" golfing hotel. "I must have looked so odd, a teenager dressed up in a bowtie, playing songs from the second world war." He loved the work and tried to find a similar job in London: unfortunately, the gay piano bar that hired him quickly decided he was "completely inappropriate – they wanted Madonna and Elton John songs, but I was in my Dr John boogie-woogie phase".

What Robins really wanted was to write and illustrate children's stories. He'd always made his own books, some of which his English teacher sent to publishers, "which was really kind, because they weren't very good". But when he began to study illustration, he grew dispirited. "They weren't interested in work being poetic or art, only in commercial illustration, specifically political cartoons." So when the opportunity arose to join Bash Street Theatre as its composer and musician, he took it.

The two years Robins then spent touring the UK and Europe taught him two things: "I didn't want to perform other people's shows – and if you think you want to make your own shows, you should just do it." The transition to solo artist was far from smooth, so he began wearing costumes: "I had a leather outfit for a character called Edward Spiderhands – like the child of Spider-Man and Edward Scissorhands. Then I did a show dressed as a transvestite monkey." When friends pointed out that the outlandish outfits just made him seem even more awkward, he switched to shadow puppetry – and suddenly audiences were captivated.

Robins's life has now come full circle: he's been commissioned to make his first children's book. With a working title of Alligator and Sausage, it will be a pop-up book with a difference, encouraging kids to fold the pages into origami boats and staircases to help characters escape from danger. Robins doesn't anticipate children reading it. "I just imagine seeing it in Tate shops and people my age buying it." But then he thinks the same about all his work: "My entire audience is made up of, I imagine, me."

• Flyboy Is Alone Again This Christmas is at the Barbican, London EC1, tonight to 2 January. Box office: 0845 120 7511.